Question

Consider a boy standing on a building that is 500m height and another boy standing on the ground. If the boy on the ground throws a ball to the boy standing on the building, with what vertical velocity must the ball be thrown such that it reaches the boy standing on the building. Neglect the height of the boys.
The kinetic energy of the ball when thrown must equal the potential energy it must gain to reach the top.

(1/2) M V^2 = M g H

V = sqrt(2 g H) = 99 m/s = 221 mph

That building is higher than the Empire State Building.

No one can throw a ball that fast. The best fast ball pitchers throw baseballs at 100 mph

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